High modulus, high strength fibers, such as Kevlar.RTM. aramid fiber and fibers of polybenzobisthiazole (PBZ) and polybenzobisoxazole (PBO) have value in composites because of their toughness and fibrillar mode of failure. Among the organic fibers, Kevlar.RTM. aramid fiber is acknowledged to have the highest compressive stress to failure as determined by in-composite performance and laboratory tests; the best of which is the single filament recoil test. (See Kumar and Helminiak, SAMPE Journal, Vol. 26, No. 2 March/April 1990 for a discussion on this subject). This has been attributed to its interchain hydrogen bonded network. Compressive performance also relates directly to shear or torsional modulus i.e., the fibers, PAN carbon and glass have close to the highest compressive properties and shear moduli and this has been attributed to their covalent or ionically crosslinked structures. The invention as disclosed herein describes a simple route to PBZ and PBO fibers that have significantly improved torsional moduli and compressive stress values (from the single filament recoil test). This should translate to better compressive properties in end uses such as composites.